A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Phi on the space of probability distributions on {1, 2,.. }. In the case of a birth-death process, the components of Phi(nu) can be written down explicitly for any given distribution nu. Using this explicit representation, we will show that Phi preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefevre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.

Stochastic models for mainland-island metapopulations in static and dynamic landscapes

This paper has three primary aims: to establish an effective means for modelling mainland-island metapopulations inhabiting a dynamic landscape: to investigate the effect of immigration and dynamic changes in habitat on metapopulation patch occupancy dynamics; and to illustrate the implications of our results for decision-making and population management. We first extend the mainland-island metapopulation model of Alonso and McKane [Bull. Math. Biol. 64:913-958,2002] to incorporate a dynamic landscape. It is shown, for both the static and the dynamic landscape models, that a suitably scaled version of the process converges to a unique deterministic model as the size of the system becomes large. We also establish that. under quite general conditions, the density of occupied patches, and the densities of suitable and occupied patches, for the respective models, have approximate normal distributions. Our results not only provide us with estimates for the means and variances that are valid at all stages in the evolution of the population, but also provide a tool for fitting the models to real metapopulations. We discuss the effect of immigration and habitat dynamics on metapopulations, showing that mainland-like patches heavily influence metapopulation persistence, and we argue for adopting measures to increase connectivity between this large patch and the other island-like patches. We illustrate our results with specific reference to examples of populations of butterfly and the grasshopper Bryodema tuberculata.

Analysis of a Local HIV-1 Epidemic in Portugal Highlights Established Transmission of non-B and -G Subtypes

Existing data supports Portugal as the Western Europe country with highest HIV-1 subtype diversity. However, detailed phylogenetic studies of Portuguese HIV-1 epidemics are still scarce. Thus, our main goal was to analyze the phylodynamics of a local HIV-1 infection in the Portuguese region of Minho. Molecular epidemiological analysis was applied to data from 289 HIV-1 infected individuals followed in the reference Hospital of the province of Minho, Portugal, in which isolated viruses had been sequenced between 2000 and 2012. Viruses of the G (29.1%) and B (27.0%) subtypes were the most frequent, followed by recombinant forms (17.6%), C (14.5%), F1 (7.3%) and A1 (4.2%) subtypes. Multinomial logistic regression revealed that the odds of being infected with A1 and F1 subtype increased over the years when compared with B, G, C or recombinant viruses. As expected, polyphyletic patterns suggesting multiple and old introductions of subtypes B and G were found. However, transmission clusters of non-B and -G viruses among native individuals were also found with the dates of the most recent common ancestor estimated to the early 2000s. Our study supports that the HIV-1 subtype diversity in the Portuguese region of Minho is high and has been increasing in a manner that is apparently driven by factors other than immigration and international travel. Infections with A1 and F1 viruses in the region of Minho are becoming established and were mainly found in sexually transmitted clusters, reinforcing the need for more efficacious control measures targeting this infection route.

A fuzzy reed-frost model for epidemic spreading

In this paper, we present a fuzzy approach to the Reed-Frost model for epidemic spreading taking into account uncertainties in the diagnostic of the infection. The heterogeneities in the infected group is based on the clinical signals of the individuals (symptoms, laboratorial exams, medical findings, etc.), which are incorporated into the dynamic of the epidemic. The infectivity level is time-varying and the classification of the individuals is performed through fuzzy relations. Simulations considering a real problem with data of the viral epidemic in a children daycare are performed and the results are compared with a stochastic Reed-Frost generalization

Detection of a new mumps virus genotype during parotitis epidemic of 2006-2007 in the State of São Paulo, Brazil

Nucleotide sequence analyses of the SH gene of 18 mumps virus isolates collected in the 2006-2007 parotitis epidemic in the state of São Paulo identified a new genotype, designated genotype M. This new designation fulfills all the parameters required to define a new mumps virus genotype. The parameters were established by an expert panel in collaboration with the World Health Organization (WHO) in 2005. This information will enhance the mumps virus surveillance program both at the national and global levels

Characterization of Dengue Virus Type 2: New Insights on the 2010 Brazilian Epidemic

Dengue viruses (DENV) serotypes 1, 2, and 3 have been causing yearly outbreaks in Brazil. In this study, we report the reintroduction of DENV2 in the coast of Sao Paulo State. Partial envelope viral genes were sequenced from eighteen patients with dengue fever during the 2010 epidemic. Phylogenetic analysis showed this strain belongs to the American/Asian genotype and was closely related to the virus that circulated in Rio de Janeiro in 2007 and 2008. The phylogeny also showed no clustering by clinical presentation, suggesting that the disease severity could not be explained by distinct variants or genotypes. The time of the most recent common ancestor of American/Asian genotype and the Sao Paulo and Rio de Janeiro (SP/RJ) monophyletic cluster was estimated to be around 40 and 10 years, respectively. Since this virus was first identified in Brazil in 2007, we suggest that it was already circulating in the country before causing the first documented outbreak. This is the first description of the 2010 outbreak in the State of Sao Paulo, Brazil, and should contribute to efforts to control and monitor the spread of DENVs in endemic areas.

Annual and polyetic progression of citrus canker on trees protected with copper sprays

The effects of copper sprays on annual and polyetic progress of citrus canker, caused by Xanthomonas citri subsp. citri, in the presence of the Asian citrus leafminer (Phyllocnistis citrella), were evaluated in a study conducted in a commercial orchard in northwest Parana state, Brazil, where citrus canker is endemic. Nonlinear monomolecular, logistic and Gompertz models were fitted to monthly disease incidence data (proportion of leaves with symptoms) for each treatment for three seasons. The logistic model provided the best estimate of disease progress for all years and treatments evaluated and logistic parameter estimates were used to describe polyetic disease dynamics. Although citrus canker incidence increased during each of the seasons studied, it decreased over the whole study period, more so in copper-treated trees than in water-sprayed controls. Copper treatment reduced disease incidence compared with controls in every year, especially 2004-2005, when incidence was ca. 10-fold higher in controls than in treated plots (estimated asymptote values 0 center dot 82 and 0 center dot 07, respectively). Copper treatment also reduced estimated initial disease incidence and epidemic growth rates every year.

High HIV incidence and prevalence among young women in rural South Africa: Developing a cohort for intervention trials

Objective: To measure prevalence and model incidence of HIV infection. Setting: 2013 consecutive pregnant women attending public sector antenatal clinics in 1997 in Hlabisa health district, South Africa. Historical seroprevalence data, 1992-1995. Methods: Serum remaining from syphilis testing was tested anonymously for antibodies to HIV to determine seroprevalence. Two models, allowing for differential mortality between HIV-positive and HIV-negative people, were used. The first used serial seroprevalence data to estimate trends in annual incidence. The second, a maximum likelihood model, took account of changing force of infection and age-dependent risk of infection, to estimate age-specific HIV incidence in 1997. Multiple logistic regression provided adjusted odds ratios (OR) for risk factors for prevalent HIV infection. Results: Estimated annual HIV incidence increased from 4% in 1992/1993 to 10% in 1996/1997. In 1997, highest age-specific incidence was 16% among women aged between 20 and 24 years. in 1997, overall prevalence was 26% (95% confidence interval [CI], 24%-28%) and at 34% was highest among women aged between 20 and 24 years. Young age (<30 years; odds ratio [OR], 2.1; p = .001), unmarried status (OR 2.2; p = .001) and living in less remote parts of the district (OR 1.5; p = .002) were associated with HIV prevalence in univariate analysis. Associations were less strong in multivariate analysis. Partner's migration status was not associated with HIV infection. Substantial heterogeneity of HIV prevalence by clinic was observed (range 17%-31%; test for trend, p = .001). Conclusions: This community is experiencing an explosive HIV epidemic. Young, single women in the more developed parts of the district would form an appropriate cohort to test, and benefit from, interventions such as vaginal microbicides and HIV vaccines.

Estimating HIV incidence rates from age prevalence data in epidemic situations

We present a method of estimating HIV incidence rates in epidemic situations from data on age-specific prevalence and changes in the overall prevalence over time. The method is applied to women attending antenatal clinics in Hlabisa, a rural district of KwaZulu/Natal, South Africa, where transmission of HIV is overwhelmingly through heterosexual contact. A model which gives age-specific prevalence rates in the presence of a progressing epidemic is fitted to prevalence data for 1998 using maximum likelihood methods and used to derive the age-specific incidence. Error estimates are obtained using a Monte Carlo procedure. Although the method is quite general some simplifying assumptions are made concerning the form of the risk function and sensitivity analyses are performed to explore the importance of these assumptions. The analysis shows that in 1998 the annual incidence of infection per susceptible woman increased from 5.4 per cent (3.3-8.5 per cent; here and elsewhere ranges give 95 per cent confidence limits) at age 15 years to 24.5 per cent (20.6-29.1 per cent) at age 22 years and declined to 1.3 per cent (0.5-2.9 per cent) at age 50 years; standardized to a uniform age distribution, the overall incidence per susceptible woman aged 15 to 59 was 11.4 per cent (10.0-13.1 per cent); per women in the population it was 8.4 per cent (7.3-9.5 per cent). Standardized to the age distribution of the female population the average incidence per woman was 9.6 per cent (8.4-11.0 per cent); standardized to the age distribution of women attending antenatal clinics, it was 11.3 per cent (9.8-13.3 per cent). The estimated incidence depends on the values used for the epidemic growth rate and the AIDS related mortality. To ensure that, for this population, errors in these two parameters change the age specific estimates of the annual incidence by less than the standard deviation of the estimates of the age specific incidence, the AIDS related mortality should be known to within +/-50 per cent and the epidemic growth rate to within +/-25 per cent, both of which conditions are met. In the absence of cohort studies to measure the incidence of HIV infection directly, useful estimates of the age-specific incidence can be obtained from cross-sectional, age-specific prevalence data and repeat cross-sectional data on the overall prevalence of HIV infection. Several assumptions were made because of the lack of data but sensitivity analyses show that they are unlikely to affect the overall estimates significantly. These estimates are important in assessing the magnitude of the public health problem, for designing vaccine trials and for evaluating the impact of interventions. Copyright (C) 2001 John Wiley & Sons, Ltd.

An epidemic of violence?: Changing patterns in reported rapes in Victoria

Victoria Police statistics show that, since the late 1980s, there has been a significant increase in reported rapes in that State. One interpretation of this trend is that there has been an increase in the underlying incidence of sexual violence in the community. An alternative explanation is that rape victims have become more willing to report to the police, in response to factors such as improved provision of support services to sexual assault victims, reforms to substantive and procedural law, and changes in police attitudes and procedures. In order to rest these competing interpretations data were collected and analysed on the characteristics of rapes reported to the Victoria Police in the late 1980s/early 1990s. This analysis showed that: (I) most of the additional offences reported in the early 1990s were allegations of rapes committed by family members, spouses and other intimates; and (2) an increasing number of reports related to offences which had been committed at feast one year prior to a report being made to the police. It is argued that these changing patterns are consistent with a significant increase in the reporting rate for rape. More generally, the research reported in this paper highlights the limitations of reported crime statistics as measures of the level of social violence, and points to the need for crime researchers to develop alternative methodologies for measuring and interpreting trends.

A fuzzy Reed-Frost model for epidemic spreading

In this paper, we present a fuzzy approach to the Reed-Frost model for epidemic spreading taking into account uncertainties in the diagnostic of the infection. The heterogeneities in the infected group is based on the clinical signals of the individuals (symptoms, laboratorial exams, medical findings, etc.), which are incorporated into the dynamic of the epidemic. The infectivity level is time-varying and the classification of the individuals is performed through fuzzy relations. Simulations considering a real problem with data of the viral epidemic in a children daycare are performed and the results are compared with a stochastic Reed-Frost generalization.

Scale-free network of a dengue epidemic

In this work we show that the dengue epidemic in the city of Singapore organized itself into a scale-free network of transmission as the 2000-2005 outbreaks progressed. This scale-free network of cluster comprised geographical breeding places for the aedes mosquitoes, acting as super-spreaders nodes in a network of transmission. The geographical organization of the network was analysed by the corresponding distribution of weekly number of new cases. Therefore, our hypothesis is that the distribution of dengue cases reflects the geographical organization of a transmission network, which evolved towards a power law as the epidemic intensity progressed until 2005. (c) 2007 Elsevier Inc. All rights reserved.

AIDS in Latin America: assessing the current status of the epidemic and the ongoing response

Background This article provides a summary of the current status of the HIV/AIDS epidemic in Latin America, as well as an outline of the diverse responses to it. Methods A search of international databases (Pubmed and ISI-Web of Science), regional databases (Scielo and Lilacs), regional and national documents and UNAIDS reports. Data are presented according to subregion. Results In Mexico HIV remains concentrated among urban men who have sex with men (MSM), and has been growing among injecting drug users (IDU) and in rural areas in relation to migration. An increasing proportion of women among those affected is observed in all countries in Central America, the most affected region, as well as increasing the impact on other vulnerable groups, such as indigenous populations. The Andean Countries have urban epidemics concentrated among MSM. In Peru, non-traditional vulnerable populations were identified. In the Southern Cone heterosexual transmission became more relevant, probably in connection with IDU epidemics and is increasingly affecting lower income groups. Incidence rates have been declining since 2002 in Brazil, the first country to guarantee free, universal access to antiretrovirals, where one-third of drug-nave patients are still initiating treatment at an advanced stage. Generally, access to treatment has improved as a result of support from the Global Fund and other initiatives, but there are concerns regarding coverage, equity and sustainability. Conclusions HIV is still concentrated among MSM in Latin America. Non-traditional vulnerable groups such as migrants and lower income populations, usually considered part of the general population, deserve attention. Programmes confronting sexual exclusion are still needed. Access to treatment has improved over time, but inequalities persist.

Multiple impacts of the HIV/AIDS epidemic on the aged in rural Uganda

This paper reports research conducted among theaged residents of a rural, Southwestern Ugandanvillage. It documents their knowledge ofHIV/AIDS, their perceptions of their own riskof infection, and the multiple impacts of thecurrent HIV/AIDS epidemic on their lives. Mostolder individuals have a sound understanding ofthe sexual transmission of HIV, and someconsider themselves to be at risk of infectionthrough having multiple sexual partners. Theyattempt to limit their children's exposure toHIV, but many of these children have left thevillage to live in urban areas of relativelyhigh HIV prevalence. The loss of adult childrendeprives the aged of any support these childrenmight have provided as their parents'capabilities declined with advancing age.Female-headed households were more affected inthis way than were male-headed households. TheAIDS epidemic has increased the number ofburials taking place in the village, and theiraccumulated costs, both in time and money, andcreated new hardships for the aged, who alsohave to cope with grief that accompaniescontinuing deaths among their children andtheir contemporaries' children.